Particle Correlations in Saturated QCD Matter

TL;DR

The paper develops an explicit eikonal framework to quantify how saturated QCD matter modifies two-parton correlations in high-energy scattering, focusing on qA collisions and the angular distribution of produced partons. By expressing two- and three-parton observables in terms of Wilson-line correlators and incorporating final-state radiation via a gluon cloud operator, it reveals a momentum-dependent transition from back-to-back to broadened, and in a narrow $p_T$ window around $Q_s$, a double-peak azimuthal structure. The results highlight a competition between perturbative Molière-like hard-scattering and coherent soft scattering of small-sized projectile components, with the latter shifting the peak away from $180^{\circ}$ and enlarging its presence for smaller projectiles. The formalism and findings pave the way for studying x-evolution effects and potential experimental signatures of saturation through two-particle correlations.

Abstract

We study quantitatively angular correlations in the two-particle spectrum produced by an energetic probe scattering off a dense hadronic target with sizeable saturation momentum. To this end, two parton inclusive cross sections for arbitrary projectiles with small color charge density are derived in the eikonal formalism. Our results are the following: For large momenta of the observed particles, the perturbative limit with characteristic back-to-back correlation is recovered. As the trigger momenta get closer to the saturation scale Q_s, the angular distribution broadens. When the momenta are significantly smaller than Q_s, the azimuthal distribution is broad but still peaked back-to-back. However, in a narrow momentum range (0.5 - 1.5) Q_s, we observe that the azimuthal correlation splits into a double peak with maxima displaced away from 180 degree. We argue that it is the soft multiple scattering physics that is responsible for the appearance of this shift in the angle of maximal correlation. We also point out that when the physical size of the projectile is particularly small, the double peak structure persists in a significantly wider range of final state momenta.

Figures (6)

• Figure 1: The full two-parton (quark-gluon) correlator (\ref{['5.12x']}) normalized to its perturbative limit (\ref{['pert2']}) as a function of the total pair momentum $K = \vert {\bf k} + {\bf p}\vert$.
• Figure 2: (a),(c): The azimuthal dependence of the quark-gluon correlator (\ref{['5.17']}) for different values of quark ($k$) and gluon ($p$) transverse momentum. The area under the curves is normalized to one, as required for differential rates per trigger particle. (b),(d): The value of the $\Delta \Phi_{kp}$-integrated double differential two-parton yield (\ref{['5.17']}), ${\rm const.} = \frac{\alpha_s\, C_F}{\pi^2} \frac{1}{(2\pi)^2}$.
• Figure 3: Angular dependence of the quark-gluon correlator (\ref{['5.17']}) for different values of the trigger momentum close to $Q_s$, ${\rm const.} = \frac{\alpha_s\, C_F}{\pi^2} \frac{1}{(2\pi)^2}$.
• Figure 4: Angular dependence of the quark-gluon correlator (\ref{['5.17']}) for different values of the trigger momentum close to $Q_s$, ${\rm const.} = \frac{\alpha_s\, C_F}{\pi^2} \frac{1}{(2\pi)^2}$. Here, the transverse size of the incoming projectile wavefunction is restricted to a small value $1/\Lambda_{\rm cut}$.
• Figure :